The present work involves the analysis of stresses generated during hydrogen charging into and discharging from Pd foil electrode.
In chapter Ⅲ, the build-up/decay of compressive and tensile stresses has been analysed as a function of hydrogen charging potential during hydrogen ingress into and egress from palladium (Pd) foil electrode in the presence of a single phase (α-Pd phase) and a mixture of two phases (α-Pd and β-Pd phases) in 0.1 M NaOH solution by using a laser beam deflection technique, combined with current transient technique. The transient of hydrogen concentration profile across the electrode is derived from the compressive and tensile deflection transients, measured simultaneously with cathodic and anodic charge transients during hydrogen ingress into the fresh electrode and hydrogen egress from the pre-charged electrode, respectively. The time to the maximum compressive and tensile deflections measured during hydrogen ingress into and egress from the electrode, respectively, is assigned to specific hydrogen concentration profiles which are characterised by the “break-through time” indicating in a first approximation the arrival of hydrogen at the opposite side of the interface. From the value of the time to the maximum deflection, hydrogen diffusivity in the Pd foil electrode was determined to be $4\times10^{-8}$ to $5\times10^{-7}cm^2 s^{-1}$. It is indicated that the elastic tensile stress field adjacent to the dislocation developed around the β-Pd phase formed in the Pd foil electrode introduces the additional trap sites for hydrogen. Larger hydrogen diffusivity determined during hydrogen discharging than hydrogen charging is discussed in terms of how much the trap sites are filled with hydrogen during hydrogen charging. Stresses exerted due to local molar volume change across the electrode during hydrogen ingress into and egress from a single α-Pd phase are always exceeded by those stresses exerted across the electrode during hydrogen ingress into and egress from a mixture of α-Pd and β-Pd phases.
In chapter Ⅳ, we measured open-circuit potential (OCP) transient and laser beam deflection transient simultaneously from the impermeable Pd foil electrode pre-charged with hydrogen at -0.08 to 0.04 V(RHE) in 0.1 M NaOH solution as a function of the pre-charging potential of hydrogen. The OCP is determined by a mixing of the potentials of two simultaneous reactions of anodic hydrogen oxidation $MH_{ads}+OH^-=M+H_2O+e_\alpha$ and cathodic hydrogen underpotential deposition $M+H_2O+e_\beta=MH_{ads}+OH^-$ below 0.15 V(RHE) and oxygen reduction $1/2O_2+ H_2O+2e_\beta=2OH^-$ above 0.15 V(RHE), coupled by a common corrosion rate. From the coincidence between the measured OCP transient and calculated corrosion potential transient, it is indicated that the plot of hydrogen oxidation rate vs. reduced time calculated corresponds to the measured OCP transient and thus both transients are closely coupled each other. This means that the hydrogen self-discharge from the electrode proceeds with the rate of hydrogen oxidation at the electrode surface, calculated based upon the mixed potential theory from the measured Evans-Hoar diagram. By taking the value of self-discharge rate on one surface determined as a function of time and adopting the impermeable constraint on the other surface as the boundary condition for hydrogen diffusion through the electrode, hydrogen concentration profile across the electrode has been derived with time from the measured tensile deflection transient.
In chapter Ⅴ, Anodic current and beam deflection transients were simultaneously measured on Pd foil electrode pre-charged with hydrogen at -0.02 and 0.09 V(RHE) in 0.1 M NaOH solution as a function of the hydrogen discharging potential. From the analysis of the anodic current transient measured, it is recognized that when the preceding potential jump in value is so low enough below the transition discharging potential, followed by subjecting the electrode surface even to a constant discharging potential, that the hydrogen concentration corresponding to the discharging potential is not fixed at the electrode surface, but the change in surface concentration with time is then given by Butler-Volmer behaviour. Based upon the hydrogen concentration profile transient simulated under the two constraints at the electrode surface depending on the discharging potential, we calculated numerically the transient of the deflection in the tensile direction caused by a smaller molar volume of $α-PdH_δ$ near the surface region than that near the inner region of the electrode during the hydrogen extraction. By comparison of the measured transient with that calculated, the movement of the maximum deflection in tensile and compressive directions was discussed in terms of the positive gradient of the molar volume between the both regions with respect to the inner direction and that negative gradient due to the formation of PdOH phase on the electrode surface, respectively.
In chapter Ⅵ, cyclic voltammogram and beam deflection transient were simultaneously measured on Pd foil electrode in 0.1 M NaOH solution as a function of scan rate. In the high scan rate range, deflection moved in the compressive direction during cathodic scan and then vanished during anodic scan, but in the low scan rate range, the deflection ran in the compressive direction during cathodic scan and rapidly down in the tensile deflection, followed by a relaxation during anodic scan. From the relationship between the anodic peak current density and scan rate, it is suggested that in the low scan rate range the hydrogen concentration gradient at the electrode surface is specified by the Butler-Volmer equation, whereas in the high scan rate range the hydrogen concentration at the electrode surface is determined by the applied potential. Based upon the hydrogen concentration profile transient simulated under the two constraints at the electrode surfaceending on sc rate, we calculated numerically the deflection transient obtained during the cyclic voltammetric measurement. The change in deflection with scan rate was discussed in terms of the positive and negative gradient of the molar volume of $α-PdH_δ$ between the electrode surface and the impermeable boundary with respect to the inner direction.
In chapter Ⅶ, the effect of stresses developed by the formation of β-PdH phase on the change in the electrode surface has been investigated by introducing the fractal dimension. The surface fractal dimension was determined by the two different electrochemical methods: One involves the diffusion-limited anodic peak current of $Fe_2+/Fe_3+$ redox reaction during cyclic voltammetry and the other is concerned with the frequency dispersion of double layer capacitance during ac-impedance spectroscopy. By using the two electrochemical methods, it is found that the surface fractal dimension was increased from about 1.97 to 2.10 with increasing fraction of $β-PdH_δ$ phase in the electrode from 0 to 1. The surface fractal dimensions obtained by using the voltammetric anodic peak current method agreed with those obtained by the analysis of the frequency dispersion of double layer capacitance.